Data-Dependent Methods for the Lag Length Selection in Unit Root Tests with Structural Change

We analyze the choice of the truncation lag for unit root tests as the  ADF^GLS  and the M^GLS tests proposed by Elliott et al. (1996) and Ng and Perron (2001) and extended to the context of structural change by Perron and Rodríguez (2003). We consider the models that allows for a change in slope and a change in the intercept and slope at unknown break date, respectively. Using Monte-Carlo experiments, the truncation lag selected according to several methods as the AIC, BIC, MAIC, MBIC is analyzed. We also include and analyze the performance of the hybrid version suggested by Perron and Qu (2007) which uses OLS instead of GLS detrended data when constructing the information criteria. All these methods are compared to the sequential t-sig method based on testing for the significance of coefficients on additional lags in the ADF autoregression. Results show that the M^GLS tests present explosive values associated with large values of the lag selected which happens more often when AIC, AIC^OLS and t-sig are used to select the lag length. The values are so negative that imply an over rejection of the null hypothesis of a unit root. On the opposite side, lag length selected using MAIC, MAIC^OLS, MBIC, MBIC^OLS methods lead to very small values of the M-tests implying very conservative results, that is, no rejection of the null hypothesis. These opposite power problems are not observed in the case of the ADF^GLS  test for which it is highly recommended.

Keywords

Unit Root Tests, Structural Change, Truncation Lag, GLS Detrending, Information Criteria, Sequential General to Specific  t-sig Method

JEL Classification

C22, C52